Acta Applicandae Mathematicae

, Volume 96, Issue 1, pp 55–69

Generalized Solutions of Nonlinear Parabolic Equations and Diffusion Processes

Authors

  • Ya. Belopolskaya
    • Department of MathematicsSt. Petersburg State University for Architecture and Civil Engineering
    • Department of Statistics, and Center for Stochastic and Chaotic Process in Science and TechnologyCase Western Reserve University
Article

DOI: 10.1007/s10440-007-9095-0

Cite this article as:
Belopolskaya, Y. & Woyczynski, W.A. Acta Appl Math (2007) 96: 55. doi:10.1007/s10440-007-9095-0

Abstract

We reduce the construction of a weak solution of the Cauchy problem for a quasilinear parabolic equation to the construction of a solution to a stochastic problem. Namely, we construct a diffusion process that allows us to obtain a probabilistic representation of a weak (in distributional sense) solution to the Cauchy problem for a nonlinear PDE.

Keywords

Stochastic flowsDiffusion processNonlinear parabolic equationsCauchy problem

Mathematics Subject Classification (2000)

60H1060J6035G0535K45

Copyright information

© Springer Science + Business Media B.V. 2007